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Mathematics > Algebraic Geometry

Title:Moderately ramified actions in positive characteristic

Abstract: In characteristic two and dimension two, wild Z/2Z-actions on k[[u,v]]
ramified precisely at the origin were classified by Artin, who showed in
particular that they induce hypersurface singularities. We introduce in this
article a new class of wild quotient singularities in any characteristic p>0
arising from certain non-linear actions of Z/pZ on the formal power series ring
in n variables. These actions are ramified precisely at the origin, and their
rings of invariants in dimension n=2 are hypersurface singularities, with an
equation of a form similar to the form found by Artin when p=2. In higher
dimension, the rings of invariants are not local complete intersection in
general, but remain quasi-Gorenstein. We establish several structure results
for such actions and their corresponding rings of invariants.